On Rings With Conditions On Nonperiodic Elements

We study commutativity of rings R with the property that for each nonperiodic element x of R there exists a positive integer K = K(x) such that x^k is central for all k≥K.     

On PP-rings

A ringR is called a leftPP-ring if every principal left ideal is projective, equivalently if the left annihilatorl(a) is generated by an idempotent for allaR. These rings seem first to have been discussed by Hattori [2] and examples include (von Neumann) regular rings and domains (possibly noncommutative). In this note we give a new characterization of leftPP-rings, use that to give an elementary proof of a result of Xue [4] characterizing triangularPP-rings, and then determine when the ringT _n (R) of upper triangular matrices overR is a leftPP-ring. Throughout the paper all rings have a unity and all modules are unitary.This research was supported by NSERC Grant A8075     

PP-理想

引入了环的PP-理想的概念,证明了PP-理想的一些性质及它与一些环、模、理想的联系,得到了一些有用的结论.     

On JB-Rings

A ring R is a QB-ring provided that aR bR=R with a,b∈R implies that there exists a y∈R such that a by∈R_q~(-1).It is said that a ring R is a JB-ring provided that R/J(R)is a QB-ring,where J(R)is the Jacobson radical of R.In this paper,various necessary and sufficient conditions,under which a ring is a JB-ring,are established.It is proved that JB-rings can be characterized by pseudo-similarity.Furthermore,the author proves that R is a JB-ring iff so is R/J(R)~2.     

On Hypertopologies

In this article a unified approach is presented to hypertopologies on collections of nonempty closed subsets of a Hausdorff uniform space generated by a saturated and separating family of pseudo-metrics. One identifies here a suitable topology on the family of proper, convex and lower semicontinuous functions defined on a Hausdorff locally convex space for which the Young Fenchel transform is bicontinuous. This improves a well known result due to Mosco, Joly and Beer.     

On cross-bandwidth

The notion of cross-bandwidth is introduced, and it is shown that any graph that is suitably contractible to a k-connected graph has cross-bandwidth at least k. The contracted edges must induce in the original graph a subgraph of maximum degree at most one. This is used to resolve a conjecture of Erdös and Chinn on the bandwidth of certain graphs.     

On HOD-supercompactness

During his Fall 2005 set theory seminar, Woodin asked whether V-supercompactness implies HOD-supercompactness. We show, as he predicted, that that the answer is no.     

On Semi-Pseudo-Ovoids

In this paper we introduce semi-pseudo-ovoids, as generalizations of the semi-ovals and semi-ovoids. Examples of these objects are particular classes of SPG-reguli and some classes of m-systems of polar spaces. As an application it is proved that the axioms of pseudo-ovoid O(n,2n,q) in PG(4n−1,q) can be considerably weakened and further a useful and elegant characterization of SPG-reguli with the polar property is given.Research Assistant of the Fund for Scientific Research Flanders (FWO-Vlaanderen)     

On FF-rings

In this paper, we study the class of rings in which every flat ideal is finitely generated. We investigate the stability of this property under localization and homomorphic image, and its transfer to various contexts of constructions such as direct products, pullback rings, and trivial ring extensions. Our results generate examples which enrich the current literature with new and original families of non-Noetherian rings that satisfy this property.     

On recurrence

Summary LetT be a non-singular ergodic automorphism of a Lebesgue space (X,L,) and letf: X be a measurable function. We define the notion of recurrence of such a functionf and introduce the recurrence setR(f)={:f– is recurrent}. If , then R()={0}, but in general recurrence sets can be very complicated. We prove various conditions for a number to lie in R(f) and, more generally, forR(f) to be non-empty. The results in this paper have applications to the theory of random walks with stationary increments.     

On formalisms

Extreme attacks on formalisms overestimate the expressive power of natural language and underestimate the power of formal languages. An overemphasis on the role of human intuition leads to an underemphasis of the value of flexible formalisms in protecting ourselves from human errors. When one uses a computer to solve problems, one builds a theory, a model of the real world, and one should use the mixture of formal and natural language that is most appropriate for the problems to be solved.Dedicated to Peter Naur on the occasion of his 60th birthday     

On UJ-rings

UJ-rings are studied, i.e., ring in which all units can be presented in a form 1+x, for some x∈J(R). The behavior of UJ-rings under various algebraic construction is investigated. In particular, it is shown that the problem of lifting the UJ property from a ring R to the polynomial ring R[x] is equivalent to the Köthe’s problem for 𝔽₂-algebras.     

关于C-环

主要讨论了 C-环的结构以及它与其它环类之间的重要关系 ,从而较深刻地刻划这种环     

On BO-algebras

In this paper, we introduce the notion of a BO-algebra, and we prove that every BO-algebra is 0-commutative, and we show that BO-algebras, 0-commutative B-algebras, BM-algebras, p-semisimple BCI-algebras and abelian groups are logically equivalent.